arXiv subjects

Srutarshi Pradhan

Publications and source records attributed to Srutarshi Pradhan.

34 records · Page 2Linked to original sources

arXiv2007

Physics Models of Earthquake

Since long back, scientists have been putting enormous effort to understand earthquake dynamics -the goal is to develop a successful prediction scheme which can provide reliable alarm that an earthquake is imminent. Model studies sometimes help to understand in some extend the basic dynamics of the real systems and therefore is an important part of earthquake research. In this report, we review several physics models which capture some essential features of earthquake phenomenon and also suggest methods to predict catastrophic events being within the range of model parameters.

cond-mat.stat-mech↗

arXiv2006

Rupture processes in fiber bundle models

Fiber bundles with statistically distributed thresholds for breakdown of individual fibers are interesting models of the static and dynamics of failures in materials under stress. They can be analyzed to an extent that is not possible for more complex materials. During the rupture process in a fiber bundle avalanches, in which several fibers fail simultaneously, occur. We study by analytic and numerical methods the statistics of such avalanches, and the breakdown process for several models of fiber bundles. The models differ primarily in the way the extra stress caused by a fiber failure is redistributed among the surviving fibers.

cond-mat.soft↗

arXiv2006

Precursors and prediction of catastrophic avalanches

In this work we review the precursors of catastrophic avalanches (global failures) in several failure models, namely (a) Fiber Bundle Model (FBM), (b) Random Fuse Model (RFM), (c) Sandpile Models and (d) Fractal Overlap Model. The precursor parameters identified here essentially reflect the growing correlations within such systems as they approach their respective failure points. As we show, often they help us to predict the global failure points in advance.

cond-mat.soft↗

arXiv2006

Crossover behavior in failure avalanches

Composite materials, with statistically distributed threshold for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution $D(Δ)$ of the magnitude $Δ$ of such avalanches. The distribution is typically a power law $D(Δ)\proptoΔ^{-ξ}$. For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent $ξ$ in the vicinity of complete breakdown and a larger exponent $ξ$ for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case $ξ=3/2$ near the breakdown point and $ξ=5/2$ away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find $ξ=2$ near the catastrophic failure and $ξ=3$ away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

cond-mat.soft↗

arXiv2005

Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

Presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility both in a equal load sharing (ELS) fiber bundle model and in local load sharing (LLS) one. We show analytically that in ELS model, the critical strength gets modified due to the presence of lower cutoff and it becomes bounded by an upper limit. Although the dynamic exponents for the susceptibility and relaxation time remain unchanged, the avalanche size distribution shows a permanent deviation from the mean-fiels power law. In the LLS model, we analytically estimate the upper limit of the lower cutoff above which the bundle fails at one instant. Also the system size variation of bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.

cond-mat.stat-mech↗

arXiv2005

Random trading market: Drawbacks and a realistic modification

We point out some major drawbacks in random trading market models and propose a realistic modification which overcomes such drawbacks through `sensible trading'. We apply such trading policy in different situations: a) Agents with zero saving factor b) with constant saving factor and c) with random saving factor --in all the cases the richer agents seem to follow power laws in terms of their wealth (money) distribution which support Pareto's observation.

physics.soc-ph↗

arXiv2005

Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure

Bundles of many fibers, with statistically distributed thresholds for breakdown of individual fibers and where the load carried by a bursting fiber is equally distributed among the surviving members, are considered. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. We show that there is, for certain threshold distributions, a crossover behavior of D(Delta) between two power laws D(Delta) proportional to Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic behavior, and we give the condition for which the D(Delta) proportional to Delta^(-3/2) behavior is seen. This crossover is a signal of imminent catastrophic failure in the fiber bundle. We find the same crossover behavior in the fuse model.

cond-mat.dis-nn↗

arXiv2004

Crossover behavior in a mixed mode fiber bundle model

We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct regimes: a) Mean-field regime where ELS mode dominates and b) short range regime dominated by LLS mode. The crossover behavior is explored through the numerical study of strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, fiber bundle model shows crossover behavior from mean-field to short range interactions.

cond-mat.stat-mech↗

arXiv2003

Precursors of catastrophic failures

We review here briefly the nature of precursors of global failures in three different kinds of many-body dynamical systems. First, we consider the lattice models of self-organised criticality in sandpiles and investigate numerically the effect of pulsed perturbations to the systems prior to reaching their respective critical points. We consider next, the random strength fiber bundle models, under global load sharing approximation, and derive analytically the partial failure response behavior at loading level less than its global failure or critical point. Finally, we consider the two-fractal overlap model of earthquake and analyse numerically the overlap time series data as one fractal moves over the other with uniform velocity. The precursors of global or major failure in all three cases are shown to be very well characterized and prominent.

cond-mat.stat-mech↗

arXiv2003

Prediction Possibility in the Fractal Overlap Model of Earthquakes

The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large events (earthquakes) in this model through the overlap time-series analysis. Taking only the Cantor sets, the overlap sizes (contact areas) are noted when one Cantor set moves over the other with uniform velocity. This gives a time series containing different overlap sizes. Our numerical study here shows that the cumulative overlap size grows almost linearly with time and when the overlapsizes are added up to a pre-assigned large event (earthquake) and then reset to `zero' level, the corresponding cumulative overlap sizes grows upto some discrete (quantised) levels. This observation should help to predict the possibility of `large events' in this (overlap) time series.

cond-mat.stat-mech↗

arXiv2003

Failure properties of fiber bundle models

We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cut-off. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

cond-mat.stat-mech↗

arXiv2003

Magnitude distribution of earthquakes: Two fractal contact area distribution

The `plate tectonics' is an observed fact and most models of earthquake incorporate that through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to reproduce the well known Gutenberg-Richter type power law in the (released) energy distribution of earthquakes. During sticking period, the elastic energy gets stored at the contact area of the surfaces and is released when a slip occurs. Therefore, the extent of the contact area between two surfaces plays an important role in the earthquake dynamics and the power law in energy distribution might imply a similar law for the contact area distribution. Since, fractured surfaces are fractals and tectonic plate- earth's crust interface can be considered to have fractal nature, we study here the contact area distribution between two fractal surfaces. We consider the overlap set of two self-similar fractals, characterised by the same fractal dimensions, and look for their distribution. We have studied numerically the specific cases of both regular and random Cantor sets in one dimension and gaskets and percolation fractals in two dimension. We find that in all the cases the distributions show an universal finite size scaling behavior. The contact area distributions have got a power law decay for both regular and random Cantor sets and also for gaskets. However, for percolation clusters the distribution shows Gaussian variation.

cond-mat.stat-mech↗

arXiv2003

Phase transition in fiber bundle models with recursive dynamics

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterised by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive the exact expressions for the order parameter, the susceptibility to changes in the initial applied sress and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

cond-mat.stat-mech↗

arXiv2003

Failure due to fatigue in fiber bundles and solids

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress. We solve this dynamics of failure analytically and show that the average failure time of the bundle decreases exponentially as the stress increases. We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress less than the bundle's strength (beyond which it fails instantly). The average failure time is again seen to decrease exponentially as the stress increases and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.

cond-mat.stat-mech↗

arXiv2001

Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure

We have studied precursors of the global failure in some self-organised critical models of sand-pile (in BTW and Manna models) and in the random fiber bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time (τ) and an average number of topplings (Δ) spread over a radial distance (ξ). We find that these quantities all depend on the average height (h_{av}) of the pile and they all diverge as (h_{av}) approaches the critical height (h_{c}) from below: (Δ) (\sim (h_{c}-h_{av}))(^{-δ}), (τ\sim (h_{c}-h_{av})^{-γ}) and (ξ) (\sim) ((h_{c}-h_{av})^{-ν}). Numerically we find (δ\simeq 2.0), (γ\simeq 1.2) and (ν\simeq 1.0) for both BTW and Manna model in two dimensions. In the strained RFB model we find that the breakdown susceptibility (χ) (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time (τ), both diverge as the applied load or stress (σ) approaches the network failure threshold (σ_{c}) from below: (χ) (\sim) ((σ_{c}) (-)(σ)^{-1/2}) and (τ) (\sim) ((σ_{c}) (-)(σ)^{-1/2}). These self-organised dynamical models of failure therefore show some definite precursors with robust power laws long before the failure point. Such well-characterised precursors should help predicting the global failure point of the systems in advance.

cond-mat.stat-mech↗

arXiv2000

A Self-organising Model of Market with Single Commodity

We have studied here the self-organising features of the dynamics of a model market, where the agents `trade' for a single commodity with their money. The model market consists of fixed numbers of economic agents, money supply and commodity. We demonstrate that the model, apart from showing a self-organising behaviour, indicates a crucial role for the money supply in the market and also its self-organising behaviour is seen to be significantly affected when the money supply becomes less than the optimum. We also observed that this optimal money supply level of the market depends on the amount of `frustration' or scarcity in the commodity market.

cond-mat.stat-mech↗